Asymptotic mean value Laplacian in metric measure spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:491

Article

Minne, Andreas¹  Tewodrose, David² 

[1] KTH Royal Inst Technol, Stockholm, Sweden

[2] Univ Cergy Pontoise, Cergy, France

关键词: Harmonic function;    Mean value property;    Metric measure space;    Maximum principle;   

DOI  :  10.1016/j.jmaa.2020.124330

来源: Elsevier

【 摘 要 】

We use the mean value property in an asymptotic way to provide a notion of a pointwise Laplacian, called AMV Laplacian, that we study in several contexts including the Heisenberg group and weighted Lebesgue measures. We focus especially on a class of metric measure spaces including intersecting submanifolds of R-n, a context in which our notion brings new insights; the Kirchhoff law appears as a special case. In the general case, we also prove a maximum and comparison principle, as well as a Green-type identity for a related operator. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free